Problem: Ashley is 27 years younger than Daniel. For the last two years, Daniel and Ashley have been going to the same school. Eighteen years ago, Daniel was 4 times as old as Ashley. How old is Daniel now?
Answer: We can use the given information to write down two equations that describe the ages of Daniel and Ashley. Let Daniel's current age be $d$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $d = a + 27$ Eighteen years ago, Daniel was $d - 18$ years old, and Ashley was $a - 18$ years old. The information in the second sentence can be expressed in the following equation: $d - 18 = 4(a - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = d - 27$ . Substituting this into our second equation, we get the equation: $d - 18 = 4($ $(d - 27)$ $ -$ $ 18)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $d - 18 = 4d - 180$ Solving for $d$ , we get: $3 d = 162$ $d = 54$.